Answer
$$e{x^{e - 1}} + {e^x}$$
Work Step by Step
$$\eqalign{
& \frac{d}{{dx}}\left( {{x^e} + {e^x}} \right) \cr
& {\text{derivative of a sum}} \cr
& = \frac{d}{{dx}}\left( {{x^e}} \right) + \frac{d}{{dx}}\left( {{e^x}} \right) \cr
& {\text{evaluate the derivative}} \cr
& = e{x^{e - 1}} + {e^x} \cr} $$
